Vector Gaussian Multiple Description with Individual and Central Receivers

TL;DR

This paper characterizes the sum rate and rate region for vector Gaussian multiple descriptions with covariance constraints, demonstrating the optimality of Gaussian descriptions and introducing a new inequality for rate bounds.

Contribution

It provides an exact characterization of the sum rate and the entire rate region for two descriptions, with a novel inequality to bound multiple description rates.

Findings

Sum rate characterized under covariance constraints

Entire rate region characterized for two descriptions

Gaussian descriptions are optimal for achieving limits

Abstract

L multiple descriptions of a vector Gaussian source for individual and central receivers are investigated. The sum rate of the descriptions with covariance distortion measure constraints, in a positive semidefinite ordering, is exactly characterized. For two descriptions, the entire rate region is characterized. Jointly Gaussian descriptions are optimal in achieving the limiting rates. The key component of the solution is a novel information-theoretic inequality that is used to lower bound the achievable multiple description rates.